There are 100 discrete intervals of integers, the i^{th} being [L_{i}, R_{i}], L_{i} and R_{i} are both positive integers and smaller than or equal to 10^{4}. From each of the intervals a number is picked at random, i.e., the probability for every number to be picked in an interval is equally likely. Find out the probability, say p, that at least 40% of the picked numbers start with the digit 1. Submit the greatest integer smaller than or equal to 100p. Get the intervals here. Format is `L_{i} R_{i}`.

Correct Answer: 1000 points

Incorrect Answer: 0 points

43200

Basic application of gradient on vectors. Consider DA, DB and DC as vectors and put their sum of gradients to zero. This will be the equilibrium condition and hence, x=y=z=120^{o}.

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